Let a and b be positive integers. Then ab=gcd(a,b)lcm(a,b). a. Please prove it and show the intermediate steps (15 pts). [Hint: Use the prime factorizations of a and b and the formulae for gcdd(a,b) and lcm(a,b) in terms of these factorizations. You also can use any other methods.] b. Verify that gcd(744,558)1cm(744,558)=744558(5pts)